Question

If three coins are tossed simultaneously, then the probability of getting at least two heads is

• A. \(\frac{1}{2}\)
• B. \(\frac{2}{3}\)
• C. \(\frac{1}{3}\)
• D. \(\frac{3}{2}\)

Answer 1

The Correct Option is A

To solve the problem, we need to determine the probability of getting at least two heads when three coins are tossed simultaneously. Let us break this down step by step.

Step 1: Understand the Sample Space When three coins are tossed, each coin has two possible outcomes: Heads (H) or Tails (T). Therefore, the total number of possible outcomes is: \[ 2 \times 2 \times 2 = 8 \] The sample space consists of all possible combinations of H and T for the three coins: \[ \{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT\} \] Step 2: Identify Favorable Outcomes We are interested in the event of getting "at least two heads." This means we need to count the outcomes that have either exactly two heads or exactly three heads.
Case 1: Exactly Two Heads The outcomes with exactly two heads are: \[ HHT, HTH, THH \] There are 3 such outcomes.
Case 2: Exactly Three Heads The outcome with exactly three heads is: \[ HHH \] There is 1 such outcome. Step 3: Count Total Favorable Outcomes The total number of favorable outcomes is the sum of the outcomes from both cases: \[ 3 \text{ (exactly two heads)} + 1 \text{ (exactly three heads)} = 4 \] Step 4: Calculate the Probability The probability of an event is given by the ratio of the number of favorable outcomes to the total number of possible outcomes: \[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{4}{8} = \frac{1}{2} \]

Final Answer: \[ {\frac{1}{2}} \]